All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
The meaning of the name “Shareed” according to the book entitled Az-Zaahir fi Ma‘rifat Kalimaat An-Naas by Al-Anbaari is as follows, “There are two possible meanings for the word “Shareed”: it may refer to a person who flees. Arabs use the past tense “sharad” to describe the stray camel if it flees from its master. Al-Asma‘i (renowned Arab scholar and anthologist, one of the earliest Arabic lexicographers and one of the three leaders of the Basri school of Arabic grammar) said that it means: 'the singular'.” [Briefly excerpted]
As for the religious ruling on giving your child this name, there is no apparent impediment because it is not an Islamically unacceptable name. The criteria for considering a name forbidden or disliked according to the Islamic Sharee'ah are the following:
The name should not express worship of, enslavement or submission to any other than Allaah such as ‘Abd Ar-Rasool (slave of the Messenger). It should not be one of the names that are particular to Allaah or an attribute of Allaah with the Arabic definite article "Al-" such as Ar-Rahmaan, Al-‘Aleem, and Malik Al-Mulook (King of kings), etc. It should not have an unpleasant meaning; and it should not imply self-praise.
For more benefit, please refer to Fataaw 87262 and 82724.
Allaah Knows best.